Optimization of the flat-field holographic concave grating in wide spectral range

Based on the geometric theory of concave grating, we deduce the mathematical expressions of the meridional curve, Sagittal curve and the relational expression for the holographic flat-field image concave grating. We also propose a new optimal method in all used range for correcting the meridional and sagittal aberrations. Different from the design method using CODE V or ZEMAX, we use mathematical expression and adopt grating optimal factor instead. By fitting the meridional focusing curve and Sagittal focusing curve of concave grating, we find an image surface in theory to ensure that the meridional and also the Sagittal aberrations tend to zero, and then design and fabricate the grating based on the fitting parameters. We solve the problem that the meridional curve transcendental equation cannot solve by Matlab, and discuss the influence of two curves for different grating constants and different incidence angles. We find that the aberrations in a wide spectral range can be corrected by diminishing the incidence angle and increasing the grating scribed lines.